The integrated Balmer lines of unresolved stellar systems have been widely used as age indicators, since they are sensitive to the temperature of the main sequence turn-off. However, the existence of “non-canonical” stellar stages such as hot horizontal branch stars and blue straggler stars (BSSs) can lead to underestimations of the true stellar population ages. Using an optimized Hβ index in conjunction with HST/WFPC2 color-magnitude diagrams (CMDs), we find that Galactic globular clusters of similar metallicity exhibit a large scatter in their Hβ strengths, which does not correlate with their CMD-derived ages. Instead, we demonstrate that the specific frequency of BSSs is responsible for the observed Hβ scatter at intermediate-to-high metallicity, in the sense that, at fixed metallicity, higher BSS ratios lead to larger integrated Hβ strengths. Therefore, the specific frequency of BSSs sets a fundamental limit on the accuracy for which integrated spectroscopic ages can be determined for globular clusters and, probably, other stellar systems like galaxies. The observational implications of this result are discussed.